A Simple Physics-Motivated Equivalent Reformulation of P=NP that Makes This Equality (Slighty) More Plausible

Authors

Jaime Nava, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

8-2011

Comments

Technical Report: UTEP-CS-11-45

Abstract

In our opinion, one of the reasons why the problem P=NP? is so difficult is that while there are good intuitive arguments in favor of P=/=NP, there is a lack of intuitive arguments in favor of P=NP. In this paper, we provide such an argument -- based on the fact that in physics, many dependencies are scale-invariant, their expression does not change if we simply change the unit in which we measure the corresponding input quantity (e.g., replace meters by centimeters). It is reasonable to imagine similar behavior for time complexity t_A(n) of algorithms A: that the form of this dependence does not change if we change change the unit in which we measure the input length (e.g., from bits to bytes). One can then easily prove that the existence of such scale-invariant algorithms for solving, e.g., propositional satisfiability is equivalent to P=NP. This equivalent reformulation of the formula P=NP is, in our opinion, much more intuitively reasonable than the original formula -- at least to those who are familiar with the importance of scale-invariance in physics.